Problem: Integrate. $ \int \sec(x)\tan(x)\,dx $ Choose 1 answer: Choose 1 answer: (Choice A) A $\sec (x) + C$ (Choice B) B $\cot (x) + C$ (Choice C) C $\tan (x) + C$ (Choice D) D $\csc (x) + C$
We need a function whose derivative is $\sec(x)\tan(x)$. We know that the derivative of $\sec(x)$ is $\sec(x)\tan(x)$, so let's start there: $\dfrac{d}{dx} \sec(x) = \sec(x)\tan(x)$ Because finding the integral is the opposite of taking the derivative, this means that: $ \int \sec(x)\tan(x)\,dx =\sec(x)\, + C$ The answer: $ \sec(x)\, + C$